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The functions f and g are defined as fol...

The functions f and g are defined as follow : `f = {(1,2),(3,5),(4,1) }` and `g = {(2,3),(5,1),(1,3)}` . Find the range of `f` and `g` . Also find the composition function `fog` and `gof`.

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The correct Answer is:
fog = {(2,5),(5,2),(1,5)}
gof = {(1,3),(3,1),(4,3)}
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KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Practice Work
  1. f : R rarr R , f(x) ={{:(2x,xgt3),(x^2,1ltxle3),(3x,xle1):} then find...

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  2. Is g= {(1, 1), (2,3), (3,5), (4,7)} a function, justify. If this is de...

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  3. The functions f and g are defined as follow : f = {(1,2),(3,5),(4,1) }...

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  4. For functions f: A rarr B and g : B rarr A , gof = IA . Prove that f i...

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  5. f: R rarr R , f(x) = x^(2)+2 and g :R rarr R , g (x) = x/(x-1) then f...

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  6. f: N rarr R , f(x) = 4x^(2) +12x +5. Show that f: N rarr R is invertib...

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  7. f and g are real valued function f(x) =x^(2) + x + 7 , x in R and g(x)...

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  8. If f is greatest integer function and g is a modulus functions the fin...

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  9. f:R rarrR , f(x) =x/(sqrt(1+x^2)),AAx inR. Then find (fofof) (x).

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  10. f : Z rarr Z and g : Z rarr Z. Defined as f(n) = 3n and g(n) = {{:(n/3...

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  11. f: R rarrR be defined by f(x) =x/2+3, g: R rarr R be defined by g(x) ...

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  12. f: Z rarrZ and g : Z rarrZ are defined as follow : f(n) ={:{(n+2," n...

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  13. ** is a binary operation on the set Q. a"*"b = (2a+b)/4 then find 2"...

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  14. ** is a binary operation on the set Q. a"*"b=a+12b+ab then find 2"*...

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  15. ** is a binary operation on the set Q. a"*"b=(a)/2+b/(3) then find ...

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  16. ** is a binary operation o Z. If x"*" y = x^(2)+y^(2)+xy then find [(...

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  17. ** be a binary operation on R defined by a"*"b = (a)/(4)+b/(7) , a,b...

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  18. Show that addition and multiplication are associative binary operation...

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  19. Find the identity element , if it exists for the following operation ....

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  20. Find the identity element , if it exists for the following operation ....

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